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CBSE Class 10 Answered

  1. Prove that  tan70º=2 tan50º +tan 20º
  2. Find the value of sin 50º-sin 70 +sinº
  3. If sinθ1 + sinθ2 +sinθ3= 3, then cosθ1 + cosθ2 +cosθ3 =?
Asked by Shambhu Nath Pandey | 11 Dec, 2015, 04:07: PM
answered-by-expert Expert Answer
1. W e space n e e d space t o space p r o v e space t h a t space tan 70 degree equals 2 tan 50 degree plus tan 20 degree C o n s i d e r space tan 90 degree colon therefore t a n 90 degree equals tan open parentheses 70 degree plus 20 degree close parentheses W e space k n o w space t h a t space tan left parenthesis A plus B right parenthesis equals fraction numerator tan A plus tan B over denominator 1 minus tan A cross times tan B end fraction therefore t a n 90 degree equals fraction numerator t a n 70 degree plus tan 20 degree over denominator 1 minus t a n 70 degree cross times t a n 20 degree end fraction rightwards double arrow infinity equals fraction numerator t a n 70 degree plus t a n 20 degree over denominator 1 minus t a n 70 degree cross times t a n 20 degree end fraction space space space space space space space open square brackets tan 90 degree equals infinity close square brackets rightwards double arrow 1 minus t a n 70 degree cross times t a n 20 degree equals 0 rightwards double arrow t a n 70 degree cross times t a n 20 degree equals 1.... left parenthesis 1 right parenthesis  A g a i n space a p p l y i n g space t h e space f o r m u l a comma space t a n left parenthesis A plus B right parenthesis comma space w e space h a v e comma t a n 70 degree equals tan open parentheses 50 degree plus 20 degree close parentheses space space space space space space space space space space space equals fraction numerator t a n 50 degree plus t a n 20 degree over denominator 1 minus t a n 50 degree cross times t a n 20 degree end fraction rightwards double arrow t a n 70 degree open parentheses 1 minus t a n 50 degree cross times t a n 20 degree close parentheses equals t a n 50 degree plus t a n 20 degree rightwards double arrow t a n 70 degree minus t a n 70 degree cross times t a n 50 degree cross times t a n 20 degree equals t a n 50 degree plus t a n 20 degree rightwards double arrow t a n 70 degree minus t a n 50 degree cross times 1 equals t a n 50 degree plus t a n 20 degree space space space space space open square brackets f r o m space e q u a t i o n space left parenthesis 1 right parenthesis close square brackets rightwards double arrow t a n 70 degree minus t a n 50 degree equals t a n 50 degree plus t a n 20 degree rightwards double arrow t a n 70 degree equals 2 t a n 50 degree plus t a n 20 degree H e n c e space p r o v e d.  P l e a s e space p o s t space o n e space q u e s t i o n space p e r space q u e r y.
Answered by Vimala Ramamurthy | 12 Dec, 2015, 01:44: PM

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